You have to visualise the problem as set problem...
Given 87 Balls with Red and Green colour
So the set equation becomes; Total (Red & Green Balls) = #Red Balls + # Green Balls - Both (Red & Green)

Given is 2/7 of Red balls also are Green ==> Both ( Red and green) = \(\frac{2}{7}\) * # Red Balls
Also it is stated that 3/5 of Green balls are red, which is again stating that ==> Both ( Red and green) = \(\frac{3}{7}\) * # Green Balls

Essentially it means that #Red Balls = \(\frac{7}{2}\)* Both (Red and Green)
Also it means that #Green Balls = \(\frac{7}{3}\)* Both (Red and Green)

Now coming back to original equation Total (Red & Green Balls) = #Red Balls + # Green Balls - Both (Red & Green)

Substituting the values we got above

87= \(\frac{7}{2}*Both + \frac{7}{3}*Both - Both\)
So Both = 18

We are asked to find Both/Total =\(\frac{18}{87}\) = \(6/29\)

Hope it helps , pls press Kudos

Still not able to understand. Could someone explain ?

Bunuel's Solution:

The easiest way would be to spot that the correct answer must have the denominator which is a factor of 87=3*29. Only D fits. You don't even need to solve anything.

Answer: D

r+g-both+none=87…r+g-both=87
2/7*r=3/7*g…r=3/2*g
3/2*g+g-3/7*g=87…5g/2-3g/7=87
35g-6g/14=87…g=87*14/29
both/total=(3/7*g)/87=(3/7*87*14/29)/87=6/29

Ans (D)